# Lexicographic Ordering

• May 3rd 2009, 04:27 AM
kurac
Lexicographic Ordering
What is this? It seems alittle confusing compared to other forms of ordering.

If we have Lex. ordering on r on A X B determined by linear order r1 on A and r2 on B. Then it would be true that if both r1 and r2 are well founded then so is r. Correct?
• May 3rd 2009, 04:44 AM
Plato
Do you understand how a dictionary is ordered?
The word “abet” comes before “about” why.
That is Lexicographic Ordering.

If we have lexicographic ordering on $\displaystyle \mathbb{N} \times \mathbb{N} \times \mathbb{N}$ here are some examples.
$\displaystyle \begin{gathered} \left( {1,3,2} \right) \prec \left( {2,1,1} \right)\text{ because } 1 < 2. \hfill \\ \left( {2,1,2} \right) \prec \left( {2,2,1} \right) \text{ because }2 = 2 \wedge 1 < 2. \hfill \\ \left( {3,3,2} \right) \prec \left( {3,3,3} \right) \text{ because }3 = 3 \wedge 3 = 3 \wedge 2 < 3. \hfill \\ \end{gathered}$

I hope this give some guidance that helps you.
• May 4th 2009, 06:02 AM
kurac